Yes. Go to Settings - Messages and disable iMessage or configure the iPad with a different iCloud account or choose to send and receive iMessage using your phone number on your iPhone and via your iCloud or Apple ID via your iPad.

You are in control to what level of connectivity you want in your Apple devices. You just need to turn your iMessages off on whatever device you don't want them to show up on but it's not an invasion of privacy. They are your devices.